A Note on Strongly Mixing Extensions
Mike Schnurr
TL;DR
This paper investigates the conditions under which strongly mixing extensions of a fixed transformation are rare, showing they are often of first category in the space of all extensions.
Contribution
It provides a new sufficient condition for strongly mixing extensions to be of first category, advancing understanding of their generic properties.
Findings
Strongly mixing extensions can be of first category under certain conditions.
A sufficient condition for the rarity of strongly mixing extensions is established.
The work extends previous investigations on generic properties of extensions.
Abstract
Continuing the investigations by the author \cite{SchnurrWM} and Glasner and Weiss \cite{GlasnerWeiss} on generic properties of extensions, we give a sufficient condition for the strongly mixing extensions of a fixed transformation to be of first category.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Finite Group Theory Research